Numerical Methods for Time-dependent PDE's
||8 credit points
||Zegeling, P. (Universiteit Utrecht)
||Basic knowledge of analysis, numerical analysis and some programming experience.
||To provide theoretical insight in, and to develop some practical skills for, numerical solution methods for evolutionary (time-dependent) partial differential equations (PDEs). Particular emphasis lies on finite difference and finite volume methods for parabolic and hyperbolic PDEs.
||The following topics will be treated:
* Classification of PDEs, basic examples and applications
* Introduction to finite differences (FDs) & basic theory: convergence, consistency and stability
* The Lax theorem and Von Neumann stability analysis
* Dispersion, dissipation and modified PDEs
* FDs for parabolic equations in one and two space dimensions
* FDs and finite volume methods for hyperbolic equations (wave-type equations)
* The method-of-lines approach
* Non-uniform and adaptive moving grids
* Higher-order and spectral methods
* Nonstandard finite-differences
* Treatment of special PDE models, such as advection-diffusion-reaction equations, fractional-order, higher-order and Hamiltonian PDEs
||Lectures (2x 45 minutes) & excercise classes (1x 45 minutes).
||The final grade is based on homework assigments & programming assignments & a final test.
||Handouts & the books (both optional) W. Hundsdorfer & J.G. Verwer, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations (Springer Series in Computational Mathematics, ISSN: 0179-3632) and Uri M. Ascher, Numerical Methods for Evolutionary Differential Equations (SIAM, 2008, Softcover, ISBN 978-0898716-52-8).